Chapter XX (part 6)

Were our space-sense more perfect in relation to any given object, say to the body of a given man, we could embrace all his life in time, from birth to death. Then within the limits of this embrace that life would be for us a constant magnitude. But now, at every given moment of it, it is for us not a constant but a variable magnitude. That which we call a body does not exist in reality. It is only the section of that four-dimensional body that we never see. We ought always to remember that our entire three-dimensional world does not exist in reality. It is a creation of our imperfect senses, the result of their imperfection. This is not the world but merely that which we see of the world. The three-dimensional world—this is the four-dimensional world observed through the narrow slit of our senses. Therefore all magnitudes which we regard as such in the three-dimensional world are not real magnitudes, but merely artificially assumed . They do not exist really, in the same way as the present does not exist really. This has been dwelt upon before. By the present we designate the transition from the future into the past. But this transition has no extension. Therefore the present does not exist. Only the future and the past exist. Thus constant magnitudes in the three-dimensional world are only abstractions, just as motion in the three-dimensional world is, in substance , an abstraction. In the three-dimensional world p. 253 there is no change, no motion. In order to think motion, we already need the four-dimensional world. The three-dimensional world does not exist in reality, or it exists only during one ideal moment. In the next ideal moment there already exists another three-dimensional world. Therefore the magnitude A in the following moment is already not A, but B, in the next C, and so forth to infinity. It is equal to itself in one ideal moment only. In other words, within the limits of each ideal moment the axioms of mathematics are true; for the comparison of two ideal moments they are merely conditional, as the logic of Bacon is conditional in comparison with the logic of Aristotle. In time , i.e., in relation to variable magnitudes, from the standpoint of the ideal moment, they are untrue. The idea of constancy or variability emanates from the impotence of our limited reason to comprehend a thing otherwise than by its section. If we would comprehend a thing in four dimensions, let us say a human body from birth to death, then it will be the whole and constant body, the section of which we call a-changing-in-time human body. A moment of life, i.e., a body as we know it in the three-dimensional world, is a point on an infinite line. Could we comprehend this body as a whole, then we should know it as an absolutely constant magnitude, with all its multifariousness of forms, states and positions; but then to this constant magnitude the axioms of our mathematics and logic would be inapplicable, because it would be an infinite magnitude. We cannot comprehend this infinite magnitude. We comprehend always its sections only . And our mathematics and logic are related to this imaginary section of the universe.